The results of the study of the influence of the conductivity of a thin film located with a certain gap above the acoustic delay line on the characteristics of propagating acoustic wave with a quasi-shear-horizontal polarization (SH0) are presented. The delay line was made of Y-X lithium niobate plate with a thickness of 200 μm containing two interdigital transducers for exciting and receiving SH0 wave. The operating frequency range of the delay line was equal to 2.6–3.8 MHz. The 1 mm thick glass plate with a film of the given conductivity applied on one plate’s side was placed above this delay line with the some air gap. The change in the phase of output signal of the delay line was measured at the various values of the width of this gap. As films with the various values of the conductivity, tin dioxide films deposited on a glass plate by high-frequency reactive magnetron sputtering in the oxygen-argon mixture were used. It has been shown that the velocity of SH0 wave propagating in the delay line under investigation depends on the film conductivity and the width of the gap between the delay line and conductive film. The dependences of the change in the SH0 wave velocity on a width of the gap between the surface of the delay line and conductive film were constructed, as well as on the film conductivity. The comparison of the experimental results with the theoretical data showed their good agreement.